What is the derivative of ax^3+bx^2-c/3 x+d ?

The derivative of ax^3+bx^2-c/3 x+d is 3ax^2+2bx-c/3

What is the first derivative of ax^3+bx^2-c/3 x+d ?

The first derivative of ax^3+bx^2-c/3 x+d is 3ax^2+2bx-c/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (a x^{3} + b x^{2} - \frac{c}{3} x + d)

3 a x^{2} + 2 b x - \frac{c}{3}

Solution steps

\frac{d}{d x} (a x^{3} + b x^{2} - \frac{c}{3} x + d)

Simplify

a x^{3} + b x^{2} - \frac{c}{3} x + d : a x^{3} + b x^{2} - \frac{c x}{3} + d

= \frac{d}{d x} (a x^{3} + b x^{2} - \frac{c x}{3} + d)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (a x^{3}) + \frac{d}{d x} (b x^{2}) - \frac{d}{d x} (\frac{c x}{3}) + \frac{dd}{d x}

\frac{d}{d x} (a x^{3}) = 3 a x^{2}

\frac{d}{d x} (b x^{2}) = 2 b x

\frac{d}{d x} (\frac{c x}{3}) = \frac{c}{3}

\frac{dd}{d x} = 0

= 3 a x^{2} + 2 b x - \frac{c}{3} + 0

Simplify

= 3 a x^{2} + 2 b x - \frac{c}{3}

What is the derivative of ax^3+bx^2-c/3 x+d ?
The derivative of ax^3+bx^2-c/3 x+d is 3ax^2+2bx-c/3
What is the first derivative of ax^3+bx^2-c/3 x+d ?
The first derivative of ax^3+bx^2-c/3 x+d is 3ax^2+2bx-c/3